Testing apparatus for scale models of aerodynamic ducts



Nbv. 25, 1952 R. LED UC 2,618,972

TESTING APPARATUS FOR SCALE MODELS OF AERODYNAMIC DUCTS 2 SHEETS-SHEET 1Filed Aug. 25, .1951

R. LEDUCQ Ndv. 25, 1952 TESTING APPARATUS FOR SCALE MODELS OFAERODYNAMIC DUCTS 2 SHEETS-SHEET 2 Filed Aug. 25, 1951Illllulfllklllallll Patented Nov. 25, 1952 TESTING APPARATUS FOR SCALEMODELS OF AERODYNAMIC DUCTS Rene Leduc, Vesinet, France ApplicationAugust 25, 1951, Serial No. 243,658 In France March 12, 1948 20 Claims.1

The present invention relates to a testing apparatus for scale models ofaerodynamic ducts, and more particularly to a model-scale duct having anouter shell beingthe replica of the outer shell of a full-scale ductoperating with combustion means,

The present application is a continuation-inpart of the co-pendingapplication Serial No. 80,337, filed March 8, 1949, now abandoned, forApparatus for Wind Tunnel Testing of Scale Models of AerothermodynamicDucts.

It is an object of the present invention to provide a model-scale ducton a reduced scale in which the effect of the combustion means in thefull-scale duct on the flow of air is limited by means operating Withoutcombustion.

It is another object of the present invention to provide a wind tunnelequipped with a tunnel balance in combination with the model-scale duct.

It is a further object of the present invention to imitate the loss inpressure suffered by the air under the influence of the combustion meansprovided in the full-scale duct. 7

A testing apparatus according to the present invention comprises in itsbroadest aspect a model-scale duct having an outer shell being thereplica of the outer shell of a full-scale duct operating withcombustion means arranged within the full-scale duct, the model-scaleduct having an entry end and an exit end, means for supporting themodel-scale duct in an air stream, and a body having a surface ofrevolution formed by a curved line, the body being arranged within themodel-scale duct substantially coaxially with the same and extendingfrom a point spaced from the entry end of the model-scale duct at leastto the exit end thereof so as to form an annular air passage between themodel-scale duct and the body, the body being shaped so that at anycrosssection perpendicular to the axis of the body the ratio of thecross-sectional area of the annular air passage between the body and themodel-scale duct to the total'internal cross-sectional area of the ductis equal to the square root of the ratio of the density of heated air atthe temper-aure prevailing a the same axial cross-section in a heatedfull-scale duct operating with combustion means to the density'of air atthe prevailing ambient temperature.

Preferably the body has a rounded leading end located substantially atthe zone of maximum cross-section of the model-scale duct.

Preferably the body includes a portion having a substantiallycylindrical and constant crosssection, the portion being located outsideand beyond the exit end of the model-scale duct.

In a preferred embodiment of the present invention, an element,preferably designed as a grid is arranged in front of the leading end ofthe body, the element restricting the flow of air through themodel-scale duct so as to imitate the loss of pressure due to thecombustion means operating in the full-scale duct.

Preferably the element is attached to the leading end of the body anddisposed perpendicularly to the axis of the model-scale duct.

A testing apparatus according to a preferred embodiment of the presentinvention comprises in combination, a wind tunnel, a model-scale ductarranged coaxially to the wind tunnel, the modelscale duct having anouter shell being the replica of the outer shell of a full-scale ductoperating with combustion means arranged at the largest cross-section ofthe full-scale duct, the modelscale duct having a variable cross-sectionincreasing from the entry end thereof to a zone of maximum cross-sectionand decreasing from the zone of maximum cross-section to the exit end ofthe model-scale duct; balancing means supporting the model-scale duct inthe air stream through the wind tunnel, a body rigidly connected to saidwind tunnel and having a surface of revolution formed by a curved line,the body being arranged within the model-scale duct substantiallycoaxially with the same and extending from a point spaced from the entryend thereof so as to form an annular air passage between the model-scaleduct and the body, the body being shaped so that at any cross-sectionperpendicular to the axis of the body the ratio of the cross-sectionalarea of the annular air passage between the body and the model-scaleduct to the total internal crosssectional area of the duct is equal tothe square root of the ratio of the density of heated air at thetemperature prevailing at the same axial cross-section in a heatedfull-scale duct operating with combustion means, to the density of airat the prevailing ambient temperature, and a portion forming part of thebody and having a substantially cylindrical constant cross-section, theportion being located outside and beyond the exit end of the model-scaleduct.

The novel features which are considered as characteristic for theinvention are set forth in particular in the appended claims. Theinvention itself, however, both as to its construction and its method ofoperation, together with additlonal objects and advantages thereof, willbe best understood from the following description 3 of specificembodiments when read in connection with the accompanying drawings, inwhich:

Fig. 1 is a sectional elevation of a full-scale duct;

Fig. 2 is a sectional elevation of a wind tunnel and a model-scale ductaccording'to the invention; and

Fig. 3 is a modification of the model-scale duct shown in Fig. 2.

Referring now to the drawings and first to Fig. l, the full-scale duct lcomprises a divergent entry diffuser 2 and a convergent exhaust nozzle3, between which the duct is provided at its maximum cross-section withinternal means t, diagrammatically represented, for heating the airflowing through it. Usually, of course, the means 4 comprise fuelburners. The air enters the duct with velocity V and is exhausted afterbeing heated by the means 4 with velocity V3, indicated by arrows. Thearrows 5 represent the internal pressures experienced by the duct-wall,such pressures being normal to the wall. The areas of a number ofcross-sections of the duct are represented by Q0, 91, 9'1, 92 and Q3.The area 90 at the entry is less than the area (23 of the nozzle exit.91 is equal to '93. and 9'1 is equal to (22.

Since S20 is less than 91:93, the axial components of the pressures 5 inthe zone Qty-42f are unbalanced. Furthermore, the normal'pressu're 5 atany section such as $22 downstream of the heating zone is less than thecorresponding pressure at a section of equal area and circumference,such as $7 upstream'of the 'he'atingz'o ne, on account of the increase"in velocity imparted to the fluid by expansion downstream of theheating zone. The forward axial components of the pressures in thedivergent part of the duct from section 01 to the heater 4 are thereforeincompletely balanced by the rearward axial components of the pressurein the convergent part of the duct downstream of the heater. The ducttherefore develops a thrust equal to the sum of all the unbalancedforward components of internal pressure, or, more accurately, equal tothe integral along the axis of the duct of the axial component of theinternal pressure multiplied by the circumference.

Referring now to Fig. 2, the model-scale duct I likewise comprising adivergent entry diffuser 2' and a convergent exhaust nozzle 3, isgeometrically similar to the full-'scaleduct. of Fig. 1. Coaxiallyplaced therein is a body 6 which extends downstream of the duct as shownat 1 to a mounting 8 such as arms connected to the wind tunnel I'Z "at alocation downstream of the model-scale duct 1 and remote from the ductwith which the arms 8, havev no physical connection, so that aerodynamicforces experienced by the body 6 are not transmitted to the tunnelbalance 9, ID.

The arms '8 cause only a small disturbance in the outflowing air sincethe arms 8 are disposed at a distance from the model-scale duct l whichis a multiple of the length model-scale duct l. The model-scale duct Iis pivoted to two links 9 and I0 forming part of the tunnel balance andhaving their other ends pivoted to a supporting element 13. The link It)is under the action of a spring ll connected to a sta tionary part M.The spring I I allows to measure the thrust exerted by the air on themodel-scale duct I.

The body 6 is so shaped that at any crosssection the cross-sectionalarea of the annulus p is the density of air at ambient temperature;

and

in which .12 is the density of air at the temperature attained in thefull-scale duct at the corresponding cross-section when operating withthe heater 4 (see Fig. 1) in action.

The leading end of the body 6 is of rounded form to prevent thegeneration of turbulence by too abrup't a change of cross-sectional areaof the air-passage, and the part of the body extending outside the ductis of cylindrical form for a considerable distance downstream, as shownin Fig. 2, in which the cross-sectional area wa is indicated as constantdownstream of the nozzle-exit. The latter feature ensures that thepresence of the body 6, 1 does not modify the character of the air-flowoutside the ductand give rise to aerodynamic forces on the model whichare unrepresentative of the full sc'ale arrangement.

In order that the forces experienced by. the duct shown in Fig. 2 maycorrectly represent those experienced by that of Fig. 1., the velocitiesat corresponding cross-sections, when reduced to the same scale must beinversely proportional to the square-roots of the corresponding air:densities p', and p, so that a VI p7 V P where V is the velocity atsection 9 in Fig. 2 without heating and V is the velocity, with heating,at the corresponding sectionof Fig. lreduced to model-scale. Further themass-flow through the duct must be the same in both cases so that themass-flow with heating across any cross-section :2 of the duct shown inFig. L'reducdto model-scale, must be equal to that withouthe'atin'gacross the corresponding annular section 9w, of the duct shown Fig. 2,so that V'(-K2e) "'VQ (3*) which by substitution from Equation 2 becomesthe Equation 1 above-stated.

It will also be evident that Equation 2 gives the relation of thevelocity V'n. at the nozzle exit of the arrangement of. Fig. :2,to thecorresponding velocity V3 in the arrangement of Fig. -1 reduced tomodel-scale.

Referring now to. Fig. 3, a modification of the body 6 of the,model-scale duct 1? is shown which is. intended to take into accountcertain differences between the real thrust which is measured and thatresulting from calculation.

It is easy to show that the thrust coefficient of a tube such as aductcan be expressed in the following form:

in which S is the surface of a plane,

W3 is the cross-sectiono'fthe gas at. avery large distance downstream oftheduct (that is, a real section in case of a full-scale duct, and

the section of the cool air'and that of the'por- I tion 1 in case of amodel-scale duct), W is the cross-sectional area of the air flow at avery large distance from the entry of the duct, A is equal to g3 and goare, respectively, the specific gravities of the air at a very largedistance downstream and upstream of the duct,

V3 and V0 are, respectively, the velocities of the air flow at the verylarge distance downstream and upstream of the duct.

The value of A can be derived from the Expression 5 by two measurementsof the total pressure downstream and upstream of the duct. However, itcan be derived also from the Expression 4 by a measurement of the thrustexerted on the duct in the wind tunnel. Generally the value of A derivedfrom the Equation 4 is smaller than that derived from the Equation 5.

In order to overcome this difiiculty a loss of pressure is createdwithin the model-scale duct by providing in the same an element such asa grid 15 which is preferably attached to the leading end of the body 6and disposed perpendicularly to the axis of the model-scale duct l. Thedimensions of the grid are determined so that the values of the term Aderived from Equations 4 and 5 are identical with each other. It can beshown that if this is the case the loss of pressure 101-192, :01 and 102being the pressures upstream and downstream of the grid, is the same asthat caused by the combusion means in the full-scale duct.

It should be noted that the grid [5 has no physical connection with themodel-scale duct l. A sufficient distance is provided between the edgeof the grid l5 and the model-scale duct I in order to eliminate anyfrictional forces which could disturb the measurements of the thrustexerted on the model-scale duct 1 which are measured for instance bymeans of the wind tunnel balance 9 to 14 shown in Fig. 2.

It will be understood that each of the elements described above, or twoor more together, may also find a useful application in other types oftesting apparatuses for aerodynamic ducts differing from the typesdescribed above.

While the invention has been illustrated and described as embodied in amodel-scale duct having an outer shell being the replica of the outershell of a full-scale duct, it is not intended to be limited to thedetails shown, since various modifications and structural changes may bemade without departing in any way from the spirit of the presentinvention.

Without further analysis, the foregoing will so fully reveal the gist ofthe present invention that others can by applying current knowledgereadily adapt it for various applications without omitting features thatfairly constitute essential characteristics of the generic or specificaspects of this invention and, therefore, such adaptations should andare intended to be comprehended within the meaning and range ofequivalence of the following claims.

What is claimed as new and desired to be secured by Letters Patent is:

1. In a testing apparatus, in combination, a model-scale duct having anouter shell being the replica of the outer shell of a full-scale ductoperating with, combustion means arranged within the full-scale duct,said model-scale duct hav- 6 ing an entry end and an exit end; means forsupporting said model-scale duct in an air stream; and a body having asurface of revolution formed by a curved line, said body being arrangedwithin said model-scale duct substantially coaxially with the same andextending from a point spaced from said entry end of said model-scaleduct at least to the exit end thereof so as to form an annular airpassage between said model-scale duct and said body, said body beingshaped so that at any cross-section perpendicular to the axis of saidbody the ratio of the cross-sectional area of said annular air passagebetween said body and said model-scale duct to the total internalcross-sectional area of said model-scale duct is equal to the squareroot of the ratio of the density of heated air at the temperatureprevailing at the corresponding axial cross-section in a heatedfull-scale duct operating with combustion means to the density of air atthe prevailing ambient temperature of said air stream.

2. In a testing apparatus, in combination, a model-scale duct having anouter shell being the replica of the outer shell of a full-scale ductoperating with combustion means arranged at the largest cross-section ofthe full-scale duct, said model-scale duct having a variablecross-section increasing from the entry end thereof to a zone of maximumcross-section and decreasing from the zone of maximum cross-section tothe exit end of said model-scale duct; means for supporting saidmodel-scale duct in an air stream; and a body having a surface ofrevolution formed by a curved line, said body being arranged within saidmodel-scale duct substantially coaxially with the same and extendingfrom a point spaced from said entry end of said model-scale duct atleast to the exit end thereof so as to form an annular air passagebetween said model-scale duct and said body, said body being shaped sothat at any cross-section perpendicular to the axis of said body theratio of the cross-sectional area of said annular air passage betweensaid body and said model-scale duct to the total internalcross-sectional area of said model-scale duct is equal to the squareroot of the ratio of the density of heated air at the temperatureprevailing at the corresponding axial cross-section in a heatedfullscale duct operating with combustion means to the density of air atthe prevailing ambient temperature of said air stream.

3. In a testing apparatus, in combination, a model-scale duct having anouter shell being the replica of the outer shell of a full-scale ductoperating with combustion means arranged at the largest cross-section ofthe full-scale duct, said model-scale duct having a variablecross-section increasing from the entry end thereof to a zone of maximumcross-section and decreasing from the zone of maximum cross-section tothe exit end of said model-scale duct; means for supporting saidmodel-scale duct in an air stream; and a body having a surface ofrevolution formed by a, curved line, said body being arranged within:said model-scale duct substantially coaxially with the same andextending from a point spaced from said entry end of said model-scaleduct at least. to the exit end thereof so as to form an annularairpassage between said model-scale duct and said body, said body beingshaped so that at any cross-section perpendicular to the axis of said.body the ratio of the cross-sectional area of said; annular air passagebetween said body and said model-scale duct to the total internalcross-sectional area of said model-scale duct is equal to smears thesquare root of the ratio of the density of heated air at the temperatureprevail-ing at the corresponding axial cross-section in a heatedii-illscale duct operating with combustion means to 4. In a testingapparatus, in combination, a

model-scale duct having an outer shell being the replica of the outershell of a full-scale duct 'op-' erating with combustion means arrangedat the largest cross-section of the full-scale duct, said model-scaleduct having a variable cross-section increasing from'the entry endthereof to axzone of maximum cross-section and decreasing from the zoneof maximum cross-section to the exit end of said model-scale duct; meansfor supporting said model-scale duct in an air stream; a body having asurfaceof revolution formed by a curved line, said body being arrangedwithin said model-scale duct substantially coaxially with the same andextending from a point spaced from said entry end of said model-scaleduct at least to the exit end thereof so as to form an annular airpassagebetween said model-scale duct and said body, said body beingshaped so that at anycross-section perpendicular to the axis of saidbody the ratio of the cross-sectional. area of said annular air passagebetween said body and said model-scale duct to the total internalcrosssectional area of said model-scale duct is equal to the square rootof the ratio of the density of heated air at the temperature prevailingat the corresponding axial cross-section in a heated full-scale ductoperating :withcombustion means to the density of airat the prevailingambient temperature of said air stream; and a portion forming part ofsaid body and having a substantially cylindrical constant cross-section,said: portionbeing located outside and beyond, the exit end ofsaidmod'el-scale duct.

'5. Inna testing apparatus, in combination, a model-scale duct having.an outer shell: being, the replicaof the outer shell of a 'full sca-leduct operating with combustion means arranged at the largestcross-section of the full-scale'duct, said model-scale duct. having avariable crosssection increasing from the entry end thereof to a zone ofmaximum cross-section and decreasingfrom the zone of maximumcross-section to the exit end of said model-scale duct; means forsupporting said model-scale duct in an air stream; a body having asurface ofrrevolution formed by a curved line, said body being arrangedwithin said modeL-scale duct substantially coaxially with the same andextending from a point spacedfrom said entry end 'of said model-scaleduct at least-to the exit end. thereof so as to form an annular airpassage between said model-scale duct and said. body, said body beingshaped so thatiat anyv cross-sectionperpendicular to theaxis of saidbody the ratioof thecross-sectional area of said annular air passagebetween said body and saidmodel scale 'duct to the totalinternalcross-sectional area of said model-scale duct is equal to-thesquare rootof th ratio of thedensity of heated air at the temperature prevailingat'the corresponding axial cross-section in aheated full-scale ductoperating with combustion means to the density of air at the prevailingambient temperature of saidairstream, said body having arounded leadingendlocated substantially at the zone-of 8 maximum cross-section of saidmodel-scale duct; and a portion for-'ming part of said bodya'nd having asubstantially cylindrical constant crosssection, said portion beinglocated outside and beyond the exit end of said model-scale duct.

6. In a testing apparatus, in combination, a model-scale duct having anouter shell being the replica of the outer shell of a full-scale ductoperating with combustion means arranged at the largest cross-section ofthe full-scale duct, said model-scale duct having a variable crossseotion increasing from the entry end thereof to a zone of maximumcross-section and decreasing. from the zone of maximum cross-section tothe exit end of said model-scale duct; means for supporting saidmodel-scale duct in an air stream; a body having a surface of revolutionformed by a curved line, said body being arranged within saidmodel-scale ducfsubstantially coaxially with the same and extending froma point spaced from said entry end of said model-scale duct at least tothe exit end thereof so as to form an annular air passage between saidmodel-scale duct and said body, said body being shaped so that at anycross-section perpendicular to the axis of said body the ratio of thecross-sectional area of said annular air passage between said body andsaid model-scale duct to the total internal cross-sectional area of saidmodel-scale duct is equal to the square root of the ratio of thedensityof heated air at a temperature pre vailing at the corresponding axialcross-section in a heated full-scale duct operating with combustionmeans to the density of air at the prevailing ambient temperature ofsaid air stream; and a portion forming part of said body and hav ing asubstantially cylindrical constant crosssection being smaller than thmaximum crosssection of said body; said portion being located outsideand beyond the exit end of said modelscale duct.

'7. In a testing apparatus, in combination, a model-scale duct having anouter shell being the replica of the outer shell of a full-scale ductoperating with combustion means arranged at th largest cross-section ofthe full-scale duct, said model-scale duct having a variablecrosssection increasing from the entry end thereof to a zone of maximumcross-section and decreasing from the zone of maximum cross-section tothe exit end of said model-scale duct; means for supporting said modelscaleduct in an air stream; a body having '.a surface of revolutionformed by acurved line, said body being arranged within said model-scaleduct substantially coaxially with the same and extending from a pointspaced from said entry end of said model-scale ductat least totheexitend thereof so as to form an annular air'passage between said modelscale ductlandv said body, said body being shaped so that at anycross-section perpendicular to the axis of said body the ratio ofthec'ross-sectional area of said annular air passage between said bodyand said model-scale duct to the total internal cross-sectional area ofsaid model-scale duct'is' equal to theisquare root of the ratio of thedensity of heated air at the temperature prevailing'at thecorresponding. axial cross-section in aheated full-scale duct operatingwith combustion means to the density of air at the prevailing ambienttemperature of said air stream,- said body having a rounded leadingendlocatedsubstantially at the zone of maximum cross section of sa-idi'nodelseale'duct; and a portion fo'rniing part of said 9 body andhaving a substantially cylindrical constant cross-section being smallerthan the maximum cross-section of said body, said portion being locatedoutside and beyond the exit of said model-scale duct.

8. In a testing apparatus, in combination, a model-scale duct having anouter shell being the replica of the outer shell of a full-scale ductoperating with combustion means arranged at the largest cross-section ofthe full-scale duct, said model-scale duct having a variablecross-section increasing from the entry end thereof to a zone of maximumcross-section and decreasing from the zone of maximum cross-section tothe exit end of said model-scale duct; means for supporting saidmodel-scale duct in an air stream; a body having a surface of revolutionformed by a curved line, said body being arranged within said modelscaleduct substantially coaxially with the same and extending from a pointspaced from said entry end of said model-scale duct at least to the exitend thereof so as to form an annular air passage between saidmodel-scale duct and said body, said body being shaped so that at anycrosssection perpendicular to the axis of said body the ratio of thecross-sectional area of said annular air passage between said body andsaid model- 'soale duct to the total internal cross-sectional area ofsaid model-scale duct is equal to the square root of the ratio of thedensity of heated air at the temperature prevailing at the correspondingaxial cross-section in a heated fullscale duct operating with combustionmeans to the density of air at the prevailing ambient temperature ofsaid air stream, said body having a rounded leading end locatedsubstantially at the zone of maximum cross-section of said modelscaleduct; and an element arranged in front of said leading end of said body,said element restricting the flow of air through said model-scale ductso as to imitate the loss of pressure due to the combustion meansoperating in the full-scale duct.

9. In a testing apparatus, in combination, a model-scale duct having anouter shell being the replica of the outer shell of a full-scale ductoperating with combustion means arranged at the largest cross-section ofthe full-scale duct, said model-scale duct having a variablecross-section increasing from the entry end thereof to a zone of maximumcross-section and decreasing from the zone of maximum cross-section tothe exit end of said model-scale duct; means for supporting saidmodel-scale duct in an air stream; a body having a surface of revolutionformed by a curved line, said body being arranged within said modelscaleduct substantially coaxially with the same and extending from a pointspaced from said entry end of said model-scale duct at least to the exitend thereof so as to form an annular air passage between saidmodel-scale duct and said body, said body being shaped so that at anycross- :section perpendicular to the axis of said body the ratio of thecross-sectional area of said annular air passage between said body andsaid model- ;scale duct to the total internal cross-sectional area ofsaid model-scale duct is equal to the square root of the ratio of thedensity of heated air at the temperature prevailing at the correspondingaxial cross-section in a heated full-scale duct operating withcombustion means to the density of air at the prevailing ambienttemperature of said air stream, said body having a rounded leading endlocated substantially .at the maximum cross-section of said modelscaleduct; and an element attached to the leading end of said body, saidelement restricting the flow of air through said model-scale duct so asto imitate the loss of pressure due to the cornbustion means operatingin the full-scale duct.

10. In a testing apparatus, in combination, a model-scale duct having anouter shell having the replica of the outer shell of a full-scale duetoperating with combustion means arranged at the largest cross-section ofthe full-scale duct, said model-scale duct having avariablecross-section increasing from the entry end thereof to a zone ofmaximum cross-section and decreasing from the zone of maximumcross-section to the exit end of said model-scale duct; means forsupporting said model-scale duct in an air stream; a body having asurface of revolution formed by a curved line, said body being arrangedwithin said model-scale duct substantially coaxially with the same andextending from a point spaced from said entry end of said model-scaleduct at least to the exit end thereof so as to form an annular airpassage between said model-scale duct and said body, said body beingshaped so that at any cross-section perpendicular to the axis of saidbody the ratio of the cross-sectional area of said annular air passagebetween said body and said model-scale duct to the total internalcross-sectional area of said model-scale duct is equal to the squareroot of the ratio of the density of heated air at the temperatureprevailing at the corresponding axial cross-section in a heatedfull-scale duct operating with combustion means to the density of air atthe prevailing ambient temperature of said air stream, said body havinga rounded leading end located substantially at the zone of maximumcross-section of said model-scale duct; and a grid arranged in front ofsaid leading end of said body, said grid restricting the flow of airthrough said model-scale duct so as to imitate the loss of pressure dueto the combustion means operating in the full-scale duct.

11. In a testing apparatus, in combination, a model-scale duct having anouter shell having the replica of the outer shell of a full-scale ductoperating with combustion means arranged at the largest cross-section ofthe full-scale duct, said model-scale duct having a variablecrosssection increasing from the entry and thereof to a zone of maximumcross-section and decreasing from the zone of maximum cross-section tothe exit end of said model-scale duct; means for supporting saidmodel-scale duct in an air stream; a body having a surface of revolutionformed by a curved zone of line, sa1d body being arranged Within saidmodel-scale duct substantially coaxially with the same and extendingfrom a point spaced from said entry end of said model-scale duct atleast to the exit end thereof so as to form an annular air passagebetween said modelscale duct and said body, said body being shaped sothat at any cross-section perpendicular to the axis of said body theratio of the cross-sectional area of said annular air passage betweensaid body and said model-scale duct to. the total internalcross-sectional area of said model-scale duct is equal to the squareroot of the ratio of the density of heated air at the temperatureprevailing at the corresponding axial cross-section in a heatedfull-scale duct operating with combustion means to the density of air atthe prevailing ambient temperature of said air stream, said body havinga rounded leading end located substantially at thezone of maximumcrosssec tion of said model-scale duct; and a grid attached to theleading end of said body, said grid restricting the flow of air throughsaid modelscale duct so as to imitate the loss of pressure due to thecombustion means operating in the full-scale duct.

12. In a testing apparatus, in combination, a model-scale duct having anouter shell having the replica of the outer shell of a full-scale ductoperating with combustion means arranged at the largest cross-section ofthe full-scale duct, said model-scale duct having a variablecrosssection increasing from the entry end thereof to av zone of maximumcross-section and decreasing from the zone of maximum cross-section tothe exit end of said model-scale duct; means for supporting saidmodel-scale duct in an air stream; a body having a surface of revolutionformed by a curved line, said body being arranged within saidmodel-scale duct substantially coaxially with the same and extendingfrom a point spaced from said entry end of said model-scale duct atleast to the exit end thereof so as to form an annular air passagebetween said model-scale duct and said body, said body being shaped sothat at any cross-section perpendicular to the axis of said body theratio of the cross-sectional area of said annular air passage betweensaid body and said model-scale duct to the total internalcross-sectionaI area of said model-scale duct is equal to the squareroot of the ratio of the density of heated air at the temperatureprevailing at the corresponding axial cross-section in a heatedfull-scale duct operating with combustion means to the density of air atthe prevailing ambient temperature of said air stream, said body havinga rounded leading end located substantially at the zone of maximumcross-section of said model-scale duct; and a grid disposedperpendicularly to the axis of said model-scale duct and arranged infront of said leading end of said body, said grid restricting the flowof air through said model-scale duct so as to imitate the loss ofpressure due to the combustion means operating inthe full-scale duct.

13. In a testing apparatus, in combination, a model-scale duct having anouter shell having the replica of the outer shell of a full-scale ductoperating with combustion means arranged at the largest cross-section ofthe full-scale duct, said model-scalev duct having a variablecrosssection increasing from the entry end thereof to a zone of maximumcross-section and decreasing from the zone of maximum cross-section tothe exit end of said model-scale duct; means for supporting saidmodel-scale duct in an air stream; a body having a surface of revolutionformed by a curved line, said body being arranged within saidmodel-scale duct substantially coaxially with the same and extendingfrom a point spaced from said entryend of said model-scale duct at leastto the exit end thereof so as to form an annular air passage betweensaid modelscale duct and said body,- said body being shaped so that atany cross-section perpendicular to the axis of said body the ratio ofthe cross-sectional area of said annular air passage between said bodyand said model-scale duct to the total internal cross-sectional area ofsaid model-scale duct is equal to the square root of the ratio of thedensity of heated air at the temperature prevailing at the correspondingaxial cross-section in a heated full-scale duct operating with combutionmeans to the density of air at the pre- 12 vailing ambient temperatureof said air stream, said body having a rounded leading end locatedsubstantially at the zone of. maximum cross-sec tion of said model-scaleduct; and a grid disposed pependicularly to the axis of said modelscaleduct and attached to the leading end of said body, said grid restrictingthe flow of air through said model-scale duct so as to imitate the lossof pressure due to the combustion means operating in the full-scaleduct.

14. A testing apparatus, comprising in combination, a wind tunnel; amodel-scale duct arranged coaxially within said wind tunnel, saidmodel-scale duct having an outer shell being the replica of the outershell of a full-scale duct operating with combusion means arranged atthe largest cross-section of the full-scale duct, said model-scale ducthaving a variable cross-section increasing fromthe entry end thereof toa zone of maximum cross-section and decreasing from the zone of maximumcross-section to the exit end-of said model-scale duct; balancing meanssupporting said model-scale duct in the air stream through said windtunnel; and a body rigidly connected to said Wind tunnel and having asurface of revolution formed by a curved line, said body being arrangedwithin said modelscale duct substantially coaxially with the same andextending from a. point spaced from said entry end of said model-scaleduct at least to the exit end thereof so as to form an annular airpassage between said model-scale duct and said body, said body beingshaped so that at any crosssection perpendicular to the axis of saidbody the ratio of the cross-sectional area of said annular air passagebetween said bod-y and said model scale duct to the total internalcross-sectional area of said mode-scale duct is equal to the square rootof the ratio of the density of heated air at the temperature prevailingat the. corresponding axial cross-section in a heated full-scale ductoperating with combustion means to the density of air at the prevailingambient temperature of said air stream.

15. A testing apparatus, comprising in combination, a wind tunnel; amodel-scale duct arranged coaxially within said wind tunnel, saidmodel-scale duct having an outer shell being the replica of the outershell of a full-scale ductoperating with combustion means arranged atthe largest cross-section of the full-scale duct, said model-scale ducthaving a variable cross-section increasing from the entry end thereof toa zone of maximum cross-section and decreasing from the zone of maximumcross-section to the exit end of said model scale duct; balancin meanssup porting said model-scale duct in the air stream through said windtunnel; a body rigidly connected to said wind tunnel and having asurface of revolution formed by a curved line, said body being arrangedwithin said model-scale duct substantially coaxially with the same andextending from a point spaced from said entry end of said model-scaleduct at least to the exit end thereof so as to form an annular airpassage between said model-scale duct and said body, said body beingshaped so that at any cross-section perpendicular to the axis of saidbody the ratio of. the crosssectional area of said annular air passagebetween said body and said model-scale duct to the total internalcross-sectional area of said duct is equal to the square root of theratio of the density of heated air at the temperatureprevailing at thesame axial cross-section in a heated full-scale duct operating withcombustion means to the density of air at the prevailing ambienttemperature; and a portion forming part of said body and having asubstantially cylindrical constant crosssection, said portion beinglocated outside and beyond the exit end of said model-scale duct andbeing rigidly connected to said wind tunnel.

16. A testing apparatus, comprising in combination, a wind tunnel; amodel-scale duct arranged coaxially within said wind tunnel, saidmodel-scale duct having an outer shell being the replica of the outershell of a full-scale duct operating with combustion means arranged atthe largest cross-section of the full-scale duct, said model-scale ducthaving a variable cross-section increasing from the entry end thereof toa zone of maximum cross-section and decreasing from the zone of maximumcross-section to the exit end of said model-scale duct; balancing meanssupporting said model-scale duct in the air stream through said windtunnel; a body rigidly connected to said wind tunnel and having asurface of revolution formed by a curved line, said body being arrangedwithin said model-scale duct substantially coaxially with the same andextending from a point spaced from said entry end of said model-scaleduct at least to the exit end thereof so as to form an annular airpassage between said model-scale duct and said body, said body beingshaped so that at any cross-section perpendicular to the axis of saidbody the ratio of the cross-sectional area of said annular air passagebetween said body and said model-scale duct to the total internalcross-sectional area of said model-scale duct is equal to the squareroot of the ratio of the density of heated air at the temperatureprevailing at the corresponding axial cross-section in a heatedfull-scale duct operating with combustion means to the density of air atthe prevailing ambient temperature of said air stream, said body havinga rounded leading end located substantially at the zone of maximumcross-section of said model-scale duct; and a portion iorming part ofsaid body and having a substantially cylindrical constant cross-section,said portion being located outside and beyond the exit end of saidmodel-scale duct and being rigidly connected to said wind tunnel.

17. A testing apparatus, comprising in combination, a wind tunnel; amodel-scale duct arranged coaxially within said wind tunnel, saidmodel-scale duct having an outer shell being the replica of the outershell of a full-scale duct operating with combustion means arranged atthe largest cross-section of the full-scale duct, said model-scale ducthaving a variable crosssection increasing from the entry end thereof toa zone of maximum cross-section and decreasing from the zone of maximumcross-section to the exit end of said model-scale duct; balancing meanssupporting said model-scale duct in the air stream through said windtunnel; a body rigidly connected to said wind tunnel and having asurface of revolution formed by a curved line, said body being arrangedwithin said model-scale duct substantially coaxially with the same andextending from a point spaced from said entry end of said model-scaleduct at least to the exit end thereof so as to form an annular airpassage between said model-scale duct and said body, said body beingshaped so that at any cross-section perpendicular to the axis of saidbody the ratio of the cross-sectional area of said annular air passagebetween said body and said model-scale duct to the total internalcross-sectional area of said model-scale duct is 75 balancing meansequal to the square root of the ratio of the density of heated air atthe temperature prevailing at the corresponding axial cross-section in aheated full-scale duct operating with combustion means to the density ofair at the prevailing ambient temperature of said air stream, said bodyhaving a rounded leading end located substantially at the zone ofmaximum crosssection of said model-scale duct; and a portion formingpart of said body and having a substantially cylindrical constantcross-section being smaller than the maximum cross-section of said body,said portion being located outside and beyond the exit end of saidmodel-scale duct and being rigidly connected to said wind tunnel.

18. A testing apparatus, comprising in combination, a wind tunnel; amodel-scale duct arranged coaxially within said wind tunnel, saidmodel-scale duct having an outer shell being the replica of the outershell of a full-scale duct operating with combustion means arranged atthe largest cross-section of the full-scale duct, said model-scale duethaving a variable crosssection increasing from the entry end thereof toa zone of maximum cross-section and decreasing from the zone of maximumcross-section to the exit end of said model-scale duct; balancing meanssupporting said model-scale duct in the air stream through said windtunnel; a body rigidly connected to said Wind tunnel and having asurface of revolution formed by a curved line, said body being arrangedwithin said model-scale duct substantially coaxially with the same andextending from a point spaced from said entry end of said model-scaleduct at least to the exit end thereof so as to form an annular airpassage between said model-scale duct and said body, said body beingshaped so that at any cross-section perpendicular to the axis of saidbody the ratio of the cross-sectional area of said annular air passagebetween said body and said model-scale duct to the total internalcross-sectional area of asid model-scale duct is equal to the squareroot of the ratio of the density of heated air at the temperatureprevailing at the corresponding axial cross-section in a heatedfull-scale duct operating with combustion means to the density of air atthe prevailing ambient temperature of said air stream, said body havinga rounded leading end located substantially at the zone of maximumcross-section of said model-scale duct; a portion forming part of saidbody and having a substantially cylindrical constant cross-section, saidportion being located outside and beyond the exit end of saidmodel-scale duct and being rigidly connected to said wind tunnel; and agrid arranged in front of said leading end of said body, said gridrestricting the flow of air through said modelscale duct so as toimitate the loss of pressure due to the combustion means operating inthe full-scale duct.

19. A testing apparatus, comprising in combination, a wind tunnel; amodel-scale duct arranged ooaxially within said wind tunnel, saidmodel-scale duct having an outer shell being the replica of the outershell of a full-scale duct operating with combustion means arranged atthe largest cross-section of the full-scale duct, said model-scale ducthaving a variable crosssection increasing from the entry end thereof toa zone of maximum cross-section and decreasing from the zone of maximumcross-section to the exit end of said model-scale duct; supporting saidmodel-scale ductiin the air stream through said wind tunnel-y a bodyrigidly connected to said wind tunnel and having a surface of revolutionformed by a curved line, said body being arranged within saidmodel-scale duct substantially coaxially with the: same and extendingfrom a point spaced from said entry end of said model-scale duct atleast to the exit end thereof so as to form an annular air passagebetween said modelscale duct and said body, said body being shaped sothat at any cross-section perpendicular to the axis of, said body theratio of the cross-sectional area of said annular air passage betweensaid body and said model-scale duct to the total in-- ternalcross-sectional area of said model-scale duct is equal to the squareroot of the ratio of the density of heated air at the temperatureprevailing at the corresponding axial cross-section in a heatedfull-scale duct operating with combustion means to the density of air atthe prevailing ambient temperature of said air stream, said body havinga rounded leading end located substantially at the zone of maximumcrosssection of said model-scale duct; a portion forming part of saidbody and having a substantially cylindrical constant cross-section, saidportion being located outside and beyond the exit end of saidmodel-scale duct and being rigidly connected to said wind tunnel; and agrid attached to the leading end of said body, said grid restricting theflow of air through said modelscaie duct so as to imitate the loss ofpressure due to the combustion means operating in the full-scale duct.

20. A testing apparatus, comprising in combination, a wind tunnel; amodel-scale duct arranged coaxially within said wind tunnel, saidmodel-scale duct having an outer shell being the replica of the outershell of a full-scale duct operating with combustion means arranged atthe largest cross-section of the full-scale duct, said model-scale ducthaving a variable cross-section increasing from the entry end thereof toa zone of maximum cross-section and decreasing from the zone of maximumcross-section to the exit end of said model-scale duct; balancing meanssupporting said model-scale duct in the air stream through said Windtunnel; a body rigidly con- 16 nected to said wind tunnel and. having asurface of revolution formed by a curved line, said body being arrangedwithin said model-scale duct substantially coaxially with the same andextending from a point spaced from said entry end of said model-scaleduct at least to the exit end thereof soas to form an annular airpassage between said model-scale duct and saidbody, said body beingshaped so that at any crosssection perpendicular to the axis of saidbody the ratio of the cross-sectional area of said annular air passagebetween said body and said modelscale duct to the. total internalcross-sectional area of said model-scale duct is equal to the squareroot of the ratio of the density of heated air at the. temperatureprevailing at the corresponding axial cross-section in a heatedfull-scale duct operating with combustion means to the density of air atthe prevailing ambient temperature of said air stream, said body havinga rounded leading end located substantially atv the zone of maximumcross-section of said modelscale duct; a portion forming part or saidbody and having a substantially cylindrical constant cross-section, saidportion being located outside and beyond the exit end of saidmodel-scale duct and bein rigidly connected to said wind tunnel; and a.grid disposed perpendicularlyto the axis of said model-scale duct andattached to the leading end of said body, said grid restricting the flowor air through said model-scale duct so as to imitate the loss ofpressure due to the combustion means operating in the full-scale duct.

RENE LEDUC.

REFERENCES GITED The following references are of record in the file ofthis patent:

UNITED STATES PATENTS

